Subgroups — C₃×C₂²⋊C₄×#1043 #72260145

Order 4800.

2064 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11716874	C₂	1	2	yes	maximal, complemented
2	C₃×C₂²⋊C₄×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₂²⋊#1043	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₃×#1043	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×C₄×#1043	C₂	1	2	yes	maximal, complemented
6	C₂²⋊C₄×#1043	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×C₅⋊D₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×#1043	—	2	4	no	—
9	C₂²×C₃×#1043	C₄	1	4	yes	complemented
10	C₂²×C₃×#1043	C₂²	1	1	yes	characteristic
11	C₂²×C₃×#1043	C₂²	1	2	yes	—
12	C₂²×C₃×#1043	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×C₅⋊D₅	C₂²	1	2	yes	—
14	C₃×C₂²⋊#1043	C₄	1	4	yes	complemented
15	C₃×C₄×#1043	—	2	4	no	—
16	C₃×C₅²×C₂²⋊C₄	C₄	1	1	yes	characteristic, complemented
17	C₃×C₂²⋊#1039	C₄	1	1	yes	characteristic, complemented
18	C₃×#87808	C₄	1	2	yes	complemented
19	C₃×C₂²⋊C₄×AGL(1,𝔽₅)	—	5	6	no	maximal
20	C₂³×#1043	C₂×C₃	1	1	yes	characteristic
21	C₂×C₂²⋊#1043	C₂×C₃	1	1	yes	characteristic
22	C₂×C₄×#1043	C₂×C₃	1	2	yes	complemented
23	C₂²⋊C₄×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
24	#11716874	C₂×C₃	1	2	yes	complemented
25	C₂³×C₃×C₅²	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×C₅⋊D₅	—	2	2	no	—
27	C₂²×C₃×C₅⋊D₅	—	2	2	no	—
28	C₂²×C₃×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₃×C₅⋊D₅	C₂×C₄	1	2	yes	—
30	C₂²×C₃×C₅⋊D₅	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₅⋊D₅	C₂³	1	1	yes	characteristic
32	C₂×C₃×#1043	—	2	2	no	—
33	C₂×C₃×#1043	—	2	2	no	—
34	C₂×C₃×#1043	—	2	2	no	—
35	C₂×C₃×#1043	—	2	8	no	—
36	C₂×C₃×#1043	C₂×C₄	1	2	yes	—
37	C₂×C₃×#1043	C₂×C₄	1	2	yes	—
38	C₂×C₃×#1043	C₂×C₄	1	4	yes	complemented
39	C₂×C₃×#1043	D₄	1	4	yes	—
40	C₂×C₃×C₄×C₅²	C₂×C₄	1	2	yes	complemented
41	C₂×C₃×#1039	C₂×C₄	1	2	yes	complemented
42	C₃×C₄×C₅⋊D₅	—	2	2	no	—
43	C₃×C₄×C₅⋊D₅	—	2	2	no	—
44	C₂³×C₃×AGL(1,𝔽₅)	—	5	6	no	—
45	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	—	5	6	no	—
46	C₂×C₃×C₄×AGL(1,𝔽₅)	—	5	12	no	—
47	C₃×D₅×C₂²⋊C₄	—	5	6	no	—
48	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	—	5	12	no	—
49	C₂³×C₅⋊D₅	C₂²×C₃	1	1	yes	characteristic
50	C₂²×#1043	—	2	4	no	—
51	C₂²×#1043	C₃×C₄	1	4	yes	complemented
52	C₂²×#1043	C₂²×C₃	1	1	yes	characteristic
53	C₂²×#1043	C₂²×C₃	1	2	yes	—
54	C₂²×#1043	C₂²×C₃	1	1	yes	characteristic
55	C₂×C₄×C₅⋊D₅	C₂²×C₃	1	2	yes	—
56	C₂²⋊#1043	C₃×C₄	1	4	yes	complemented
57	C₄×#1043	—	2	4	no	—
58	C₅²×C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic, complemented
59	C₂²⋊#1039	C₃×C₄	1	1	yes	characteristic, complemented
60	#87808	C₃×C₄	1	2	yes	complemented
61	C₂²⋊C₄×AGL(1,𝔽₅)	—	5	6	no	—
62	C₂²×C₃×C₅²	—	2	2	no	—
63	C₂²×C₃×C₅²	C₄²	1	2	yes	complemented
64	C₂²×C₃×C₅²	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₃×C₅⋊D₅	—	2	2	no	—
66	C₂×C₃×C₅⋊D₅	—	2	2	no	—
67	C₂×C₃×C₅⋊D₅	—	2	2	no	—
68	C₂×C₃×C₅⋊D₅	—	2	4	no	—
69	C₂×C₃×C₅⋊D₅	C₄²	1	2	yes	complemented
70	C₂×C₃×C₅⋊D₅	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₃×C₅⋊D₅	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₃×C₅⋊D₅	C₂×D₄	1	2	yes	—
73	C₂×C₃×C₅⋊D₅	#41	1	2	yes	—
74	C₃×#1043	—	2	2	no	—
75	C₃×#1043	—	2	4	no	—
76	C₃×#1043	C₂²⋊C₄	1	4	yes	direct product factor
77	C₃×C₄×C₅²	—	2	2	no	—
78	C₃×#1039	—	2	2	no	—
79	C₂³×C₃×D₅	—	5	6	no	—
80	C₂²×C₃×AGL(1,𝔽₅)	—	5	6	no	—
81	C₂²×C₃×AGL(1,𝔽₅)	—	5	24	no	—
82	C₂²×C₃×AGL(1,𝔽₅)	—	5	12	no	—
83	C₂²×C₃×AGL(1,𝔽₅)	—	5	6	no	—
84	C₂²×C₃×AGL(1,𝔽₅)	—	10	24	no	—
85	C₂×C₃×C₄×D₅	—	5	12	no	—
86	C₃×C₂²⋊AGL(1,𝔽₅)	—	5	24	no	—
87	C₃×C₄×AGL(1,𝔽₅)	—	10	24	no	—
88	C₃×C₅×C₂²⋊C₄	AGL(1,𝔽₅)	1	6	yes	complemented
89	C₃×C₂²⋊Dic₅	—	5	6	no	—
90	C₃×#685	—	5	12	no	—
91	C₂³×C₅²	C₂×C₃×C₄	1	1	yes	characteristic
92	C₂²×C₅⋊D₅	—	2	2	no	—
93	C₂²×C₅⋊D₅	—	2	2	no	—
94	C₂²×C₅⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
95	C₂²×C₅⋊D₅	C₂×C₃×C₄	1	2	yes	—
96	C₂²×C₅⋊D₅	C₂×C₃×C₄	1	2	yes	—
97	C₂²×C₅⋊D₅	C₂³×C₃	1	1	yes	characteristic
98	C₂×#1043	—	2	2	no	—
99	C₂×#1043	—	2	2	no	—
100	C₂×#1043	—	2	2	no	—
101	C₂×#1043	—	2	8	no	—
102	C₂×#1043	C₂×C₃×C₄	1	2	yes	—
103	C₂×#1043	C₂×C₃×C₄	1	2	yes	—
104	C₂×#1043	C₂×C₃×C₄	1	4	yes	complemented
105	C₂×#1043	C₃×D₄	1	4	yes	—
106	C₂×C₄×C₅²	C₂×C₃×C₄	1	2	yes	complemented
107	C₂×#1039	C₂×C₃×C₄	1	2	yes	complemented
108	C₄×C₅⋊D₅	—	2	2	no	—
109	C₄×C₅⋊D₅	—	2	2	no	—
110	C₃×C₄×C₂²⋊C₄	—	25	1	no	Hall
111	C₂³×AGL(1,𝔽₅)	—	5	6	no	—
112	C₂×C₂²⋊AGL(1,𝔽₅)	—	5	6	no	—
113	C₂×C₄×AGL(1,𝔽₅)	—	5	12	no	—
114	D₅×C₂²⋊C₄	—	5	6	no	—
115	(C₂×AGL(1,𝔽₅))⋊C₄	—	5	12	no	—
116	C₂×C₃×C₅²	—	2	2	no	—
117	C₂×C₃×C₅²	C₂×C₄²	1	1	yes	characteristic
118	C₂×C₃×C₅²	C₄×D₄	1	2	yes	—
119	C₃×C₅⋊D₅	—	2	2	no	—
120	C₃×C₅⋊D₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₃×C₅⋊D₅	#117	1	1	yes	characteristic
122	C₃×C₅⋊D₅	C₄×D₄	1	2	yes	—
123	C₂³×C₃×C₅	C₂×AGL(1,𝔽₅)	1	6	yes	—
124	C₂²×C₃×D₅	—	5	6	no	—
125	C₂²×C₃×D₅	—	5	12	no	—
126	C₂²×C₃×D₅	—	5	12	no	—
127	C₂²×C₃×D₅	—	5	6	no	—
128	C₂²×C₃×D₅	—	10	12	no	—
129	C₂²×C₃×D₅	—	10	12	no	—
130	C₂×C₃×AGL(1,𝔽₅)	—	5	12	no	—
131	C₂×C₃×AGL(1,𝔽₅)	—	5	24	no	—
132	C₂×C₃×AGL(1,𝔽₅)	—	5	12	no	—
133	C₂×C₃×AGL(1,𝔽₅)	—	5	24	no	—
134	C₂×C₃×AGL(1,𝔽₅)	—	10	48	no	—
135	C₂×C₃×AGL(1,𝔽₅)	—	10	12	no	—
136	C₂×C₃×AGL(1,𝔽₅)	—	10	12	no	—
137	C₂×C₃×AGL(1,𝔽₅)	—	10	12	no	—
138	C₂×C₃×C₄×C₅	C₂×AGL(1,𝔽₅)	1	12	yes	complemented
139	C₂×C₃×Dic₅	—	5	12	no	—
140	C₃×C₄×D₅	—	10	12	no	—
141	C₃×C₄×D₅	—	10	12	no	—
142	C₂²×C₅²	—	2	2	no	—
143	C₂²×C₅²	C₃×C₄²	1	2	yes	complemented
144	C₂²×C₅²	C₂²×C₃×C₄	1	1	yes	characteristic
145	C₂×C₅⋊D₅	—	2	2	no	—
146	C₂×C₅⋊D₅	—	2	2	no	—
147	C₂×C₅⋊D₅	—	2	2	no	—
148	C₂×C₅⋊D₅	—	2	4	no	—
149	C₂×C₅⋊D₅	C₃×C₄²	1	2	yes	complemented
150	C₂×C₅⋊D₅	C₂²×C₃×C₄	1	1	yes	characteristic
151	C₂×C₅⋊D₅	C₂²×C₃×C₄	1	1	yes	characteristic
152	C₂×C₅⋊D₅	C₂×C₃×D₄	1	2	yes	—
153	C₂×C₅⋊D₅	C₃×#41	1	2	yes	—
154	#1043	—	2	2	no	—
155	#1043	—	2	4	no	—
156	#1043	C₃×C₂²⋊C₄	1	4	yes	direct product factor
157	C₄×C₅²	—	2	2	no	—
158	#1039	—	2	2	no	—
159	C₂³×C₃×C₄	—	25	1	no	—
160	C₂×C₃×C₂²⋊C₄	—	25	1	no	—
161	C₂×C₃×C₂²⋊C₄	—	25	1	no	—
162	C₂×C₃×C₄²	—	25	2	no	—
163	C₃×#95	—	25	2	no	—
164	C₂³×D₅	—	5	6	no	—
165	C₂²×AGL(1,𝔽₅)	—	5	6	no	—
166	C₂²×AGL(1,𝔽₅)	—	5	12	no	—
167	C₂²×AGL(1,𝔽₅)	—	5	24	no	—
168	C₂²×AGL(1,𝔽₅)	—	5	6	no	—
169	C₂²×AGL(1,𝔽₅)	—	10	24	no	—
170	C₂×C₄×D₅	—	5	12	no	—
171	C₂²⋊AGL(1,𝔽₅)	—	5	24	no	—
172	C₄×AGL(1,𝔽₅)	—	10	24	no	—
173	C₅×C₂²⋊C₄	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
174	C₂²⋊Dic₅	—	5	6	no	—
175	#685	—	5	12	no	—
176	C₃×C₅²	C₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
177	C₄×C₂²⋊C₄	—	25	1	no	Sylow
178	C₂²×C₃×C₅	—	2	12	no	—
179	C₂²×C₃×C₅	C₄×AGL(1,𝔽₅)	1	12	yes	complemented
180	C₂²×C₃×C₅	C₂²×AGL(1,𝔽₅)	1	6	yes	—
181	C₂×C₃×D₅	—	5	6	no	—
182	C₂×C₃×D₅	—	5	6	no	—
183	C₂×C₃×D₅	—	5	12	no	—
184	C₂×C₃×D₅	—	5	12	no	—
185	C₂×C₃×D₅	—	5	12	no	—
186	C₂×C₃×D₅	—	10	12	no	—
187	C₂×C₃×D₅	—	10	12	no	—
188	C₂×C₃×D₅	—	10	24	no	—
189	C₂×C₃×D₅	—	10	12	no	—
190	C₃×AGL(1,𝔽₅)	—	5	24	no	—
191	C₃×AGL(1,𝔽₅)	—	10	12	no	—
192	C₃×AGL(1,𝔽₅)	—	10	24	no	—
193	C₃×C₄×C₅	—	2	12	no	—
194	C₃×Dic₅	—	10	12	no	—
195	C₂×C₅²	—	2	2	no	—
196	C₂×C₅²	C₂×C₃×C₄²	1	1	yes	characteristic
197	C₂×C₅²	C₃×C₄×D₄	1	2	yes	—
198	C₅⋊D₅	—	2	2	no	—
199	C₅⋊D₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
200	C₅⋊D₅	C₃×#117	1	1	yes	characteristic
201	C₅⋊D₅	C₃×C₄×D₄	1	2	yes	—
202	C₂⁴×C₃	—	25	1	no	—
203	C₂²×C₃×C₄	—	25	1	no	—
204	C₂²×C₃×C₄	—	25	1	no	—
205	C₂²×C₃×C₄	—	25	2	no	—
206	C₂²×C₃×C₄	—	25	4	no	—
207	C₂²×C₃×C₄	—	25	2	no	—
208	C₂²×C₃×C₄	—	50	4	no	—
209	C₃×C₂²⋊C₄	—	25	4	no	—
210	C₃×C₂²⋊C₄	—	25	1	no	—
211	C₃×C₂²⋊C₄	—	25	2	no	—
212	C₃×C₂²⋊C₄	#1043	1	1	yes	characteristic, direct product factor
213	C₃×C₄²	—	50	4	no	—
214	C₂³×C₅	C₂×C₃×AGL(1,𝔽₅)	1	6	yes	—
215	C₂²×D₅	—	5	6	no	—
216	C₂²×D₅	—	5	12	no	—
217	C₂²×D₅	—	5	12	no	—
218	C₂²×D₅	—	5	6	no	—
219	C₂²×D₅	—	10	12	no	—
220	C₂²×D₅	—	10	12	no	—
221	C₂×AGL(1,𝔽₅)	—	5	12	no	—
222	C₂×AGL(1,𝔽₅)	—	5	24	no	—
223	C₂×AGL(1,𝔽₅)	—	5	12	no	—
224	C₂×AGL(1,𝔽₅)	—	5	24	no	—
225	C₂×AGL(1,𝔽₅)	—	10	48	no	—
226	C₂×AGL(1,𝔽₅)	—	10	12	no	—
227	C₂×AGL(1,𝔽₅)	—	10	12	no	—
228	C₂×AGL(1,𝔽₅)	—	10	12	no	—
229	C₂×C₄×C₅	C₂×C₃×AGL(1,𝔽₅)	1	12	yes	complemented
230	C₂×Dic₅	—	5	12	no	—
231	C₄×D₅	—	10	12	no	—
232	C₄×D₅	—	10	12	no	—
233	C₂³×C₄	—	25	1	no	—
234	C₂×C₂²⋊C₄	—	25	1	no	—
235	C₂×C₂²⋊C₄	—	25	1	no	—
236	C₂×C₄²	—	25	2	no	—
237	#95	—	25	2	no	—
238	C₂×C₃×C₅	—	2	12	no	—
239	C₂×C₃×C₅	C₂×C₄×AGL(1,𝔽₅)	1	6	yes	—
240	C₂×C₃×C₅	D₄×AGL(1,𝔽₅)	1	12	yes	—
241	C₃×D₅	—	5	6	no	—
242	C₃×D₅	—	5	6	no	—
243	C₃×D₅	—	5	12	no	—
244	C₃×D₅	—	10	12	no	—
245	C₅²	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
246	C₂³×C₃	—	25	1	no	—
247	C₂³×C₃	—	25	2	no	—
248	C₂³×C₃	—	25	2	no	—
249	C₂³×C₃	—	25	1	no	—
250	C₂³×C₃	—	50	2	no	—
251	C₂³×C₃	—	50	2	no	—
252	C₂³×C₃	C₂×#1043	1	1	yes	characteristic
253	C₂×C₃×C₄	—	25	4	no	—
254	C₂×C₃×C₄	—	25	2	no	—
255	C₂×C₃×C₄	—	25	4	no	—
256	C₂×C₃×C₄	—	25	2	no	—
257	C₂×C₃×C₄	—	25	2	no	—
258	C₂×C₃×C₄	—	50	2	no	—
259	C₂×C₃×C₄	—	50	2	no	—
260	C₂×C₃×C₄	—	50	8	no	—
261	C₂×C₃×C₄	—	50	2	no	—
262	C₂×C₃×C₄	—	50	2	no	—
263	C₂×C₃×C₄	—	50	2	no	—
264	C₂×C₃×C₄	C₂×#1043	1	2	yes	complemented
265	C₂²×C₅	—	2	12	no	—
266	C₂²×C₅	C₃×C₄×AGL(1,𝔽₅)	1	12	yes	complemented
267	C₂²×C₅	C₂²×C₃×AGL(1,𝔽₅)	1	6	yes	—
268	C₂×D₅	—	5	6	no	—
269	C₂×D₅	—	5	6	no	—
270	C₂×D₅	—	5	12	no	—
271	C₂×D₅	—	5	12	no	—
272	C₂×D₅	—	5	12	no	—
273	C₂×D₅	—	10	12	no	—
274	C₂×D₅	—	10	12	no	—
275	C₂×D₅	—	10	24	no	—
276	C₂×D₅	—	10	12	no	—
277	AGL(1,𝔽₅)	—	5	24	no	—
278	AGL(1,𝔽₅)	—	10	24	no	—
279	AGL(1,𝔽₅)	—	10	12	no	—
280	C₄×C₅	—	2	12	no	—
281	Dic₅	—	10	12	no	—
282	C₂⁴	—	25	1	no	—
283	C₂²×C₄	—	25	1	no	—
284	C₂²×C₄	—	25	1	no	—
285	C₂²×C₄	—	25	2	no	—
286	C₂²×C₄	—	25	4	no	—
287	C₂²×C₄	—	25	2	no	—
288	C₂²×C₄	—	50	4	no	—
289	C₂²⋊C₄	—	25	4	no	—
290	C₂²⋊C₄	—	25	1	no	—
291	C₂²⋊C₄	—	25	2	no	—
292	C₂²⋊C₄	C₃×#1043	1	1	yes	characteristic, direct product factor
293	C₄²	—	50	4	no	—
294	C₃×C₅	C₂²⋊C₄×AGL(1,𝔽₅)	1	6	yes	complemented
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	25	1	no	—
297	C₂²×C₃	—	25	1	no	—
298	C₂²×C₃	—	25	2	no	—
299	C₂²×C₃	—	25	2	no	—
300	C₂²×C₃	—	25	2	no	—
301	C₂²×C₃	—	50	2	no	—
302	C₂²×C₃	—	50	4	no	—
303	C₂²×C₃	—	50	2	no	—
304	C₂²×C₃	—	50	2	no	—
305	C₂²×C₃	C₄×#1043	1	2	yes	complemented
306	C₂²×C₃	C₂²×#1043	1	1	yes	characteristic
307	C₃×C₄	—	2	2	no	—
308	C₃×C₄	—	25	4	no	—
309	C₃×C₄	—	50	4	no	—
310	C₃×C₄	—	50	2	no	—
311	C₃×C₄	—	50	2	no	—
312	C₂×C₅	—	2	12	no	—
313	C₂×C₅	C₂×C₃×C₄×AGL(1,𝔽₅)	1	6	yes	—
314	C₂×C₅	C₃×D₄×AGL(1,𝔽₅)	1	12	yes	—
315	D₅	—	5	6	no	—
316	D₅	—	5	6	no	—
317	D₅	—	5	12	no	—
318	D₅	—	10	12	no	—
319	C₂³	—	25	1	no	—
320	C₂³	—	25	1	no	—
321	C₂³	—	25	2	no	—
322	C₂³	—	25	2	no	—
323	C₂³	—	50	2	no	—
324	C₂³	—	50	2	no	—
325	C₂³	C₂×C₃×#1043	1	1	yes	characteristic
326	C₂×C₄	—	25	4	no	—
327	C₂×C₄	—	25	2	no	—
328	C₂×C₄	—	25	4	no	—
329	C₂×C₄	—	25	2	no	—
330	C₂×C₄	—	25	2	no	—
331	C₂×C₄	—	50	2	no	—
332	C₂×C₄	—	50	2	no	—
333	C₂×C₄	—	50	8	no	—
334	C₂×C₄	—	50	2	no	—
335	C₂×C₄	—	50	2	no	—
336	C₂×C₄	—	50	2	no	—
337	C₂×C₄	C₂×C₃×#1043	1	2	yes	complemented
338	C₂×C₃	—	2	2	no	—
339	C₂×C₃	—	25	1	no	—
340	C₂×C₃	—	25	2	no	—
341	C₂×C₃	—	25	1	no	—
342	C₂×C₃	—	50	2	no	—
343	C₂×C₃	C₂×C₄×#1043	1	1	yes	characteristic
344	C₂×C₃	D₄×#1043	1	2	yes	—
345	C₅	C₃×C₂²⋊C₄×AGL(1,𝔽₅)	1	6	yes	complemented
346	C₂²	—	2	2	no	—
347	C₂²	—	25	1	no	—
348	C₂²	—	25	1	no	—
349	C₂²	—	25	2	no	—
350	C₂²	—	25	2	no	—
351	C₂²	—	25	2	no	—
352	C₂²	—	50	2	no	—
353	C₂²	—	50	4	no	—
354	C₂²	—	50	2	no	—
355	C₂²	—	50	2	no	—
356	C₂²	C₃×C₄×#1043	1	2	yes	complemented
357	C₂²	C₂²×C₃×#1043	1	1	yes	characteristic
358	C₄	—	2	2	no	—
359	C₄	—	25	4	no	—
360	C₄	—	50	2	no	—
361	C₄	—	50	4	no	—
362	C₄	—	50	2	no	—
363	C₃	C₂²⋊C₄×#1043	1	1	yes	characteristic, direct product factor, Sylow
364	C₂	—	2	2	no	—
365	C₂	—	25	1	no	—
366	C₂	—	25	2	no	—
367	C₂	—	25	1	no	—
368	C₂	—	50	2	no	—
369	C₂	C₂×C₃×C₄×#1043	1	1	yes	characteristic
370	C₂	C₃×D₄×#1043	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×#1043
commutator	C₂×C₅²	C₂×C₃×C₄²
Frattini	C₂²	C₂²×C₃×#1043
Fitting	C₃×C₅²×C₂²⋊C₄	C₄
socle	C₂²×C₃×C₅²	C₂²×C₄
prime radical	C₂³×C₃×C₅⋊D₅	C₂²
cosocle	C₂²×C₅⋊D₅	C₂³×C₃
hypercenter	C₃×C₂²⋊C₄	#1043
hypocenter	C₅²	C₃×C₄×C₂²⋊C₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₂²⋊C₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×#11716874	C₂	semidirect
5. C₂×C₃×C₄×#1043	C₂	semidirect
6. C₂²⋊C₄×#1043	C₃	direct (N × H)
9. C₂²×C₃×#1043	C₄	semidirect
14. C₃×C₂²⋊#1043	C₄	semidirect
16. C₃×C₅²×C₂²⋊C₄	C₄	semidirect
17. C₃×C₂²⋊#1039	C₄	semidirect
18. C₃×#87808	C₄	semidirect
22. C₂×C₄×#1043	C₂×C₃	semidirect
24. #11716874	C₂×C₃	semidirect
38. C₂×C₃×#1043	C₂×C₄	semidirect
40. C₂×C₃×C₄×C₅²	C₂×C₄	semidirect
41. C₂×C₃×#1039	C₂×C₄	semidirect
51. C₂²×#1043	C₃×C₄	semidirect
56. C₂²⋊#1043	C₃×C₄	semidirect
58. C₅²×C₂²⋊C₄	C₃×C₄	semidirect
59. C₂²⋊#1039	C₃×C₄	semidirect
60. #87808	C₃×C₄	semidirect
63. C₂²×C₃×C₅²	C₄²	semidirect
69. C₂×C₃×C₅⋊D₅	C₄²	semidirect
76. C₃×#1043	C₂²⋊C₄	direct (N × H)
88. C₃×C₅×C₂²⋊C₄	AGL(1,𝔽₅)	semidirect
104. C₂×#1043	C₂×C₃×C₄	semidirect
106. C₂×C₄×C₅²	C₂×C₃×C₄	semidirect
107. C₂×#1039	C₂×C₃×C₄	semidirect
138. C₂×C₃×C₄×C₅	C₂×AGL(1,𝔽₅)	semidirect
143. C₂²×C₅²	C₃×C₄²	semidirect
149. C₂×C₅⋊D₅	C₃×C₄²	semidirect
156. #1043	C₃×C₂²⋊C₄	direct (N × H)
173. C₅×C₂²⋊C₄	C₃×AGL(1,𝔽₅)	semidirect
176. C₃×C₅²	C₄×C₂²⋊C₄	semidirect
179. C₂²×C₃×C₅	C₄×AGL(1,𝔽₅)	semidirect
212. C₃×C₂²⋊C₄	#1043	direct (N × H)
229. C₂×C₄×C₅	C₂×C₃×AGL(1,𝔽₅)	semidirect
245. C₅²	C₃×C₄×C₂²⋊C₄	semidirect
264. C₂×C₃×C₄	C₂×#1043	semidirect
266. C₂²×C₅	C₃×C₄×AGL(1,𝔽₅)	semidirect
292. C₂²⋊C₄	C₃×#1043	direct (N × H)
294. C₃×C₅	C₂²⋊C₄×AGL(1,𝔽₅)	semidirect
305. C₂²×C₃	C₄×#1043	semidirect
337. C₂×C₄	C₂×C₃×#1043	semidirect
345. C₅	C₃×C₂²⋊C₄×AGL(1,𝔽₅)	semidirect
356. C₂²	C₃×C₄×#1043	semidirect
363. C₃	C₂²⋊C₄×#1043	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#11716874	2
C₃×C₂²⋊C₄×C₅⋊D₅	2
C₂×C₃×C₂²⋊#1043	2
C₂³×C₃×#1043	2
C₂×C₃×C₄×#1043	2
C₂²⋊C₄×#1043	3
C₃×C₂²⋊C₄×AGL(1,𝔽₅)	5

Subgroups — C3×C22⋊C4×#1043 #72260145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂²⋊C₄×#1043 #72260145